Enveloping worm gearing



May 10, 1960 Filed Dec. 10, 1957 E. WILDHABER ENVELOPING WORM GEARING 3 Sheets-Sheet 1 INVENTOR.

l I I May 10, 1960 E. WILDHABER 2,935,888

ENVELOPING WORM GEARING Filed Dec. 10, 1957 3 Sheets-Sheet 2 EM. w'vwwe,

May 10, 1960 E. WILDHABER 2,935,888

ENVELOPING WORM GEARING Filed Dec. 10, 1957 3 Sheets-Sheet 3 INVENTOR.

ENVELOPING WORM GEARING Ernest Wildhaher, Brighton, N .Y. Application December 10, 1957, Serial No. 701,792 19 Claims. (Cl. 74-458) The present invention relates to enveloping worm gearmg containing an hourglass or throated worm and a wormgear having a concave root line in an axial section.

The present invention is based, in part, upon the same principles as disclosed in my applications Enveloping Worm Gearing Serial No. 682,804 and No. 695,623, filed September 9, 1957 and November 12, 1957 respectively, and relates, in general, to the same type of gearing.

It has been commonly assumed that in conventional Cone or Hindley worm gearing the tooth contact is in the midplane of the wormgear and extends through the entire length of the worm. Applicant has demonstrated mathematically, however, that the tooth contact, which carries the load, follows a diagonal path. In the Cone or Hindley enveloping worm gearing this path crosses the center line of the worm gearing; and the point where this path crosses the center line is one end of the path of tooth contact. Applicant has demonstrated mathematically that at this point in the midplane of the wormgear the contacting tooth surfaces are almost counterparts of one another.

it is at this point, however, in the Cone or Hindley type worm gearing that the mating tooth surfaces start to intersect and interfere with one another. They intersect in the midplane of the wormgear. They intersect at small angles which vary along the length of the worm. The only reason that the tooth surfaces of the Cone or Hindley worm and wormgear do not interfere with one another beyond the midplane is because the interfering portions are automatically cut away in the production of the wormgear; for it is the conventional practice to hob the wormgear with a hob essentially like the worm; and such a hob will automatically produce wormgear teeth that will mesh with a worm, that corresponds to the hob, without interference with the thread of the worm. Nevertheless, because the interfering tooth portions are cut away the tooth contact ceases at the midplane in the conventional Cone or Hindley type'worm gearing. At most, therefore, only half the length of the wormgear teeth will be in contact during operation. This limits the load-carrying capacity of such gearing and afiects its life.

Furthermore for producing the Cone or Hindley wormgears a different hob is required for each different diameter, lead angle, and pitch of worm in order to correctly produce a correctly mating worm gear.

Other known types. of enveloping worm gearing are either difficult and expensive to produce, and/or also are limited in their load-carrying capacity and life.

One object of the present invention is to devise enveloping wonn gearing having a high load-carrying capacity and a long duration of contact, and that has improved adjustment characteristics.

The tooth bearing, or load-carrying area, is shifted on the teeth when the gear pair is inaccurately mounted or made and when it yields somewhat under load. The shift of the tooth bearing depends on the kind of inaccuracy incurred, such as a small mounting error in the H d. St e Pa n 2,935,888 Patented May 19, 1960 direction of either oneof the two axes of the gear pair, or in the direction of the center line of the gear pair, or an error in the angular setting; In general the bearing shift is both lengthwise and depthwise of the teeth, and different for difierent displacements.

An aim of the present invention is to provide a tooth shape for enveloping worm gearing such that there is only one kind of tooth-bearing shift, a shift longitudinally of the teeth, and where the bearing shift due to one kind of mounting displacement may be compensated by an opposite shift due to another kind of displacement.

A further object of the present invention is to devise enveloping worm gearing that can be produced efiiciently and with relatively simple tools, and that permits the use of standard tools not specific to a member of the wormgear pair. Hitherto it was customary to provide a hob representing the worm of the pair.

Up to now difficulties'increased with increasing helix angle of the wormgear teeth. A further aim is to devise worm gearing in which large helix angles can be handled with ease.

Worm gearing with large worms, both throated and cylindrical worms, have always provided difiiculties to accurate manufacture, because of the frightening cost of the large hobs representing the worms. A further aim is to do away with such difficulties.

Another object is to devise worm gearing conjugate to a basic member, where both the worm and wormgear are capable of contacting and meshing with the tooth surfaces of said basic member, and where said surfaces have a constant profile in all axial sections and a constant profile in all cross-sections at right angles to the axis of the basic member.

7 A still further aim is to provide a tooth shape based on a basic member of constant normal base pitch at all points of its tooth surfaces, and on a basic member having involute helical tooth surfaces, or on a circular rack havaims may be attained singly or in any combination.

Inthe drawings:

Fig. 1 is a diagrammatic plan view of a worm and wormgear embodying the invention, showlng thewormgear in axialsection, the drawing plane containing the Wormgear axis and being parallel to the worm axis.

Fig. 2 is a fragmentary front elevational VIEW-COHE- sponding to Fig. 1, looking along the wormgear ax1s, and a diagram showing the mesh.

Fig. 3 is a section taken at right angles to the worm axis and containing the wormgear axis, corresponding to Fi 1.

Fig. 4 is a fragmentary and diagrammatic view along its axis of the helical member shown in Fig. 1.

Fig. 5 is a diagram illustrating conjugacy of the worm and wormgearwith anex'ternal helical member and an imaginary counterpart internal helical member respectively.

Figures 6 and 7 are fragmentary axial sections of a wormgear, showing the kind of tooth bearing displacements aimed at.

Fig. 8 is a view similar to Fig. 1, showing diagrammatically a rotary tool in engagement with the wormgear.

Fig. 9 is a diagrammatic view of a pair of reciprocatory tools such as may be. substituted for the tool shown in Fig. 8.

' Fig. 10 is a fragmentary end view of another form of tool.

Figures 11, 12 and 13 are diagrammatic plan views comparing different'embodiments of thepresent invention.

Fig. 14 is a diagrammatic plan view similar to Fig. l,

but referring to a modification, the wormgear being shown in axial section.

Fig. is a fragmentary front elevational view corresponding to Fig. 14, showing also a diagrammatic view of the mesh.

Fig. 16 is a fragmentary axial section of the wormgear and a view taken along the worm axis from the right in Fig. 1.

Fig. 17 is an axial view of the threaded helical member also shown in Fig. 14, on which the tooth shape of the worm gearing is based.

Fig. 18 is a diagrammatic plan view taken in the same direction as Fig. 14, and showing a rotary tool in engagement with the worm.

Referring first to the embodiment illustrated in Figures 1 to 4, numeral 21 denotes a throated worm having a minimum diameter at its gorge or throat 22, and meshing with a wormgear 23. The latter has a root surface of concave axial profile 24. That is the tooth bottoms follow a surface of revolution coaxial with the wormgear 23 and containing profile 24. The worm 21 and wormgear 23 are rotatably mounted on axes 25 and 26 respectively, which in the instance illustrated are at right angles to one another.

The teeth 56 of the wormgear and the teeth or threads 28 of the worm areformed for intimate tooth contact, mating tooth surfaces being so closely matched that there is a tendency to interfere with each other.

In my aforesaid application Serial No. 695,623 a definite interference line is assumed in a suitable position on the worm thread. It moves with the worm thread and is part thereof. The tooth shape of the wormgear is then the path of this interference line relatively to the wormgear, and is thus determined. The worm is formed conjugate to this wormgear to transmit uniform motion be tween them. Its shape can be determined from the tooth shape of the wormgear, as described in said application. This tooth shape has a surface of action which extends diagonally across the region of the intermeshing teeth. Each side surface of the worm thread consists of a working portion and a smaller relieved portion. The two portions meet at the assumed interference line.

Here now we start out from a surface of action similar to the one determined from a given interference line on the thread surface of the worm. Control of the surface of action is achieved through selection of a suitable basic member, whose tooth surfaces are "adapted to contact the worm and wormgear along the same lines along which the worm and wormgear contact each other.

The basic member'30 contains coaxial involute helical tooth surfaces 31 or thread surfaces. The profiles 32 (Fig. 4) in any plane perpendicular to its axis 33 are involutes of a base circle 34.

The determination of this member will now be described, so as to achieve a path of contact 35 suitably inclined to the worm axis 25. Path 35 intersects the center line 36 of the wormgear pair at a point 40, which may be referred to as the pitch point. It lies in a plane 37 parallel to the axes 25 and 26 and perpendicular to center line 36. The latter intersects the axes 25, 26 at right angles, at points 41, 42.

The path of contact 35 is chosen at an inclination i to the direction of the worm axis 25; i being smaller than the helix angle h of the wormgear teeth to the direction of the wormgear axis 26. Angle h is also the inclination of the projected tooth-surface normal at 40 to the worm axis 25 (Fig. 1). Inclination i may be chosen approximately according to the equation tan i= /2 tan h 'tance from point 45a.

with path 35 proportional to the pitch radii 40-41 and 4042, Fig. 3. Line 43 intersects the projected axes 25, 26 at points 44, 45 respectively, and path 35 at point 40. The distances 40'-44 and 40-45 should then be in the same proportion as the pitch radii r=40-41 and R:40-42. When the axes 25, 26 are at right angles this general relation can be expressed by the simple formula tan g= etn i Only one side of the teeth need be considered, as the two sides are alike. One side can be brought into the others position by turning the worm or wormgear about center line 36 through half a turn.

The axis 33 of basic member 30 is perpendicular to the above determined line 43 and intersects line 43 at 46a. It intersects center line 36 at 39 and is offset from the gear axis a distance 39-42 proportional to distance 46a45 at the same ratio as the pitch radius R is proportional to distance 40'--45.

In view of this construction a plane 44-45 perpendicular to axis 33 intersects the axes 25, 26 at points 44a, 45a of a straight line which also contains point 40 of the path 35 aand point 46a of axis 33.

It will now be shown why the so determined member 30 is a basic member, adapted to contact the worm and wormgear along the same lines along which they contact each other.

It is obvious that common contact exists at pitch point 40, for the helical teeth 47 are so determined. Point 40' of said sectional plane 44-45 is a point of contact between the worm and wormgear and member 30, if the common surface normal 50' has leverages with respect to the three axes 25, 26, 33 in the proportion of the tooth numbers of the respective members. In other words, a given force acting along tooth normal 50' should produce turning moments in the same proportion as tooth surface normal 50 at pitch point 40. With the assumed involute helical teeth 47 on member 30 not only the same proportions, but the same turning moments are produced at any point 40' as at pitch point 40. The given force can be resolved into a component in the direction of axis 33, perpendicular to the drawing plane of Fig. 4, and into a component lying in the drawing plane. Both components remain. constant. The axial component lies in plane 37. It retains the same direction therein, and the same distances from the three axes 25, 26, 33 respectively as at point 40. Therefore the respective turning moments produced by this axial force component remain the same as at point 40.

The force component in the sectional plane 44-45 is tangent to base circle 34 (Fig. 4) and produces a constant turning momenton helical member 30. This component is offset from point 45a of axis 26 a distance larger than the radius 0 of base circle 34. It compares with base radius 0 as distance 4045a compares with distance 4033 (Fig. 4). The proportion of these two distances is constant. Accordingly the considered component has a constant distance from point 45a. The turning moment produced on the wormgear in the sectional plane 44-45 is produced by a constant force that has a constant dis- It is constant.

In the same way it can be shown that the turning moment produced in the sectional plane on the worm is constant. This then establishes any point 40' of straight path 35 as a common contact point between all three members, and line 35 as the path of contact in plane 37. And always normal 50 is an element of the surface of action.

While this proof is based on involute teeth on member 30, which is the preferred form of teeth, it can be demonstrated thatthe basic member can be determined in the same way when teeth of other profile shape are used.

This form of basic member represents a special caseof the basic helical members referred to in'my application Gearing, Serial No. 544,270, filed November 1, 1955.

Any surface normal (50') at a contact point (40) stays normal to the involute helical tooth surfaces of basic member at all turning positions of member 30, and continues to fulfill the kinematic condition of contact. During such turning motion the point of contact moves uniformly on the normal. The normal therefore lies in the common surface of action between the worm, wormgear and basic member. The surface of action or its extension contains path and all the surface normals at the various points 40, 40" etc. of said path. These normals 50, 50 etc. are all tangent to a cylindrical surface coaxial with member 30 and containing base circle 34 (Fig. 4). And they have a constant inclinationfrom axis 33 of member 30.

The useful part of the path of contact 35 is shown in full lines. The useful surface of action contains the normals (50', 50, 50") that intersect the said useful part of path 35 and that lie within reach of the contacting teeth. This actual surface of action extends diagonally across the zone of interengagement of the teeth, at an angle to each of the two axes of the wormgear pair.

A mean path of contact, intermediate the outside surfaces of mating teeth, is shown in dotted lines 57 (Fig. 1). It bypasses the center line (36) and extends in a general direction parallel to path 35.

As described. especially in application Serial No. 682,804 the contact between the worm and wormgear is very intimate at point 40 of center line 36. This is also true for allother points of normal 50 within the region of mesh. This normal represents one end of the surface of action, the end with the best contact.

To avoid interference, the thread sides of the worm should be relieved starting at the spiral line (52, Fig. 2) and continuing to the adjacent end of the thread. Spiral 52 of thread side '53 is the intersection of fixed normal 50 with the rotating thread side. The latter thus contains a working portion and a relieved portion 54.

The thread sides generally follow the profile inclination of the wormgear teeth and have a varying inclination to planes perpendicular to the worm axis 25 and parallel to the end planes 55, The relieved portion (54) is provided in the region of least inclination. The relief may be just large enough to avoid interference and contact thereon. Y V

The opposite thread side 53' is identical with side 53.

The pitch point 40, where the surface of action intersects the center line 36, is preferably placed adjacent the root surface of the wormgear. That is, the tooth surfaces of the wormgear and those of basic member 30 are placed chiefly on the outside of the pitch circle that passes through pitch point 40. This increases the actual surface of action and region of contact. The surface of action contains all the normals 50, 50', 50" etc. and is seen to come closer to the center line 36 of the wormgear pair adjacent the outside surface of the worm thread than at the inner end of the working portion of the thread.

The surface of action intersects the drawing plane of Fig. 3 in a line 58. This plane contains the wormgear axis 26 and is the central plane of rotation of the worm. The surface of action of the opposite side of the mating teeth intersects this plane in a line 58'. The two lines 58, 58 converge towards pitch point 40. The surface of action and the mean path of contact (57) extend about axis 33 at an approximately constant distance therefrom. The tooth action ends or starts at normal 50. Only the dotted portion above and to the left of projected normal 50 (Fig. 3) is the inactive part of the gear tooth surface.

It should also be noted that the inner end of spiral 52, adjacent the thread bottom, has a larger distance from the central plane of rotation of the worm than the outer end of said spiral. Also therelieved thread portion 54 is seen to be longer at the;.outside.surface 21 of'the worm 21 than adjacent its root; surface.

While the worm 21 is fully conjugate to the external basic member 30 in conventional manner, the wormgear 23 is fully conjugate to the same helical tooth surfaces of the same member in a different way. It can be consideredconjugate to an imaginary internal member 30' (Fig. 4) that fully matches the external member 30 and is the counterpart thereof. Member 30' is imaginary because actual physical contact is not possible. The tooth surfaces would interfere with each other. This condition is illustrated'in Fig. 5. The profile of the basic memher is shown in dotted lines 62. If embodied as the profile of an external member, this convex profile contacts a normal way with the concave profile 60 of the worm. But when embodied as the profile of a counterpart internal member, the concave profile 62 is more curved than the convex profile 61 of the wormgear it should contact. Contact is possible only on paper, in imagination. Yet this concept is very useful, as will be evident hereafter. The inside diameter of the internal member 30 is seen to be smaller than the mean root diameter of the conjugate wormgear 23.

Thus far fully conjugate tooth surfaces have been referred to, where a pair of mating tooth surfaces contact along a line which sweeps the entire working portion as the worm and wormgear run together. This full tooth bearing, the area swept by the line of contact, is sensitive to even slight inaccuracies of tooth shape and mounting, and to deflections under load. For this reason it is customary to provide a restricted or localized tooth hearing, which is less sensitive. The teeth are somewhat eased off adjacent their boundaries, by known slight changes in manufacture. Such gearing is still conjugate in the sense that uniform motion is transmitted as accurately as practically feasible and that a substantial tooth hearing area is achieved.

. Fig. 6 shows a tooth bearing 63 obtained by easing off the tooth ends 64, but having no ease-off depthwise of the teeth 65. It is marked with criss-cross lines. Fig. 7 shows a tooth bearing 66 where depthwise ease-off or profile ease-off is added.

The tooth bearings 63, 66 shift on the tooth surfaces when the worm and wormgear are inaccurately mounted or yield under load. This shift increases with increasing tooth-bearing area. It is a purpose of the present invention to provide a toothshape whose bearing-shift is only in one direction, lengthwise of the teeth (65). There should be only this one kind of shift, regardless of whether a slight displacement occurs in the direction of the worm axis, or in the direction of the wormgear axis, or in the direction of the center line, or in the shaft angle. Then different displacements may often partially or wholly compensate one another. And very little, if any, depthwise ease-off or profile-ease-off is required.

A further object is to provide a tooth shape well suited for the self-adjusting mounting described in my expired Patent No. 2,069,433, grantedFebruary 2, 1937. Such mounting permits the practical use of nearly full tooth bearings.

Shifted tooth bearings are indicated in dotted lines 63', 66 in Figures 6 and 7 respectively. In Fig. 6'the center 67 of the tooth bearing is shown shifted to a position 67' lengthwise of the teeth 65. In Fig. 7 bearing center 68 is-shown shifted to 68'. There should be no depthwise shift to a position such as 682.

The gear mesh and the'adjustment characteristics depend on the tooth-surface normals. Each of these normals, or perpendiculars to the tooth surface, has a definite leverage with respect to the axis of the member. The leverage can be measured by the turning moment exerted about this axis by a given constant force. Ordinarily the various normals of for instance the gear-tooth surface have difierent leverages.

In operation a point of the gear-tooth surface contacts a definite point of the mating worm-thread surface. The normals at the contacting points are so interrelated that 7 their leverages are in the proportion of the numbers of teeth and threads, as required by kinematics. They could not otherwise contact at the given turning ratio.

This requirement remains in effect upon adjustment or slight displacement of the gears. A considered point of the gear-tooth surface can contact at the turning ratio prescribed by the tooth numbers only such points of the worm-thread surface, whose normals have the leverage proportion of the tooth numbers.

There are therefore two requirements for contact at a given point, the described kinematic requirement and the obvious geometric requirement for contact.

The described tooth shape however is based on an involute helical member (30) whose surface normals have all the same constant leverage. The surface normals of any gear or member fully conjugate to this member also have a constant leverage, in the proportion of the respective tooth numbers. Thus the worm 21 and the Wormgear 23 each contain tooth surface normals of constant leverage.

There is therefore no kinematic restriction. Each point of a wormgear-tooth side can properly contact each point of a mating thread-side of the worm. Here there are not two conditions of contact, but only one, the geometric condition or requirement. And there is only one kind of bearing shift, the one shown in Figures 6 and 7, as can be further demonstrated.

This applies to all described embodiments of the invention. A constant leverage can also be expressed as a constant normal base pitch, a constant pitch along the tooth surface normals.

Production To produce the wormgear 23 a single-threaded hob 70 (Fig. 8) may be used. It is shown in a central position, where its axis 71 intersects the center line 36. In principle the hob thread should be an involute helicoid. But a conventional thread with straight axial section 72 differs only immaterially from it. Normal 50 represents the line of action between the hob thread and the wormgear, in the shown central position. Hob 70 can properly contact the wormgear 23 because the latter has convex profiles. The hob is then so fed that its straight line of action successively covers all the normals (58, 50', 50") of the surface of action. It is fed angularly about axis 33 of basic member 36 and moved in the direction of axis 33, while the timing is changed to conform to the different position.

To effect a line of action coinciding with normal the hob 70 is fed about axis 33 (Fig. 4) through an angle b and moved along said axis so that its point 49 coincides with point 73, where normal 50' intersects the cylindrical pitch surface 69 of member 36. The timing change is proportional to the turning angle 12 and differently proportional to the axial displacement, as readily understood.

The hob outline is then in a position indicated in dotted lines 70 in Fig. 8, its axis being at 71. The former intersection point of the hob axis with center line 36 is then at 72. Distance 4i -46d measures the axial displacement. Other lines of action are similarly covered.

The cut preferably starts at one end of the surface of action, such as the left end. The hob 70 is bodily fed about axis 33 and lengthwise of said axis until it reaches the shown central position. By then it has cut the part of the considered side of the teeth which gets into working contact with the worm. Preferably the hob thread is made thick enough that it contacts both sides of the wormgear teeth in the central position. As the turning feed about axis 33 goes on the axial feed is preferably made to conform to the opposite side of the teeth. In this way the working portions of both sides of the teeth are completed when the hob reaches the (right) end of its feed.

The remaining portions of the wormgear teeth have no 8. work to do and may be relieved somewhat, if desired. This is exactly what happens in the described process. To form the remaining portion so as to correspond to the extension of path 35 a different hob position along axis 33 would be required than for forming the working portion of the opposite side. The change in axial position to suit the opposite side of the teeth produces a relief in this case. Accordingly the wormgear may be finished in a single feed pass.

In place of a hob 70, a reciprocatory tool of rack form could also be used, and reciprocated along plane 37 (Fig. 2) so that in the middle position the cutting edges describe normal 50. It cuts while the wormgear rotates uniformly, and returns to starting position while out of engagement with the wormgear, at every stroke. The feed motions about and along axis 33 are the same as described for hob 7 0.

Fig. 9 shows another form of reciprocatory tools. The tools 120, 121 reciprocate along the surface normals 50, 50 of opposite tooth sides, in the middle position, outing in the directions of arrows 122, 123 respectively while the work piece rotates uniformly on its axis. Here also the tools are disengaged completely from the work piece during their return strokes. Here also the described feed motions about and along axis 33 are provided. Also 'a complete stroke cycle with return should preferably correspond to uniform rotation of the wormgear through an integral number of teeth or pitches, which number should beprime to the tooth number of the worm gear.

A rotating gear-shaped cutter 100, Fig. 10, may also be used in place of the tools described. It may have an axis 101 perpendicular to the plane of the drawing. Or it may have an axis 101' tilted to effect relief, while retaining a cylindrical outside surface on its cutting teeth 102. a

The working portions of worm 21 may be produced with a tool which directly embodies the basic helical member 30. The tool may be either a rotary hob or a shaper tool that performs a helical reciprocation. The relief (at 54) may be applied to the worm threads either in a separate operation, or it may be bu'dt into said hob. Also a gear-shaped cutter (100, Fig. 10) may be used to cut the worm in an operation similar to the one described for hob 70. The cutter is fed about and along the axis 33 of the basic member. With cutters or tools of this kind it is unnecessary for the basic member to have an integral number of teeth.

Comparison lDiagram Fig. 11 shows in huge enlargement an infiniteslmal portion of a plane like plane 37 of Fig. l. The embodiment just described approximates a worm gearing where a definite interference line is assumed on the worm thread and moves with the worm thread. Point 40 of this interference line moves about the worm axis 25 at right angles thereto, in the direction of the projected wormgear axis 26. The path of contact 35 then has the described inclination i; and the inclination g of the axis 33 of the basic member can be constructed with a line 43' that intersects path 35 and the projected axes 25, 26 at points 40a, 44' and 45' respectively. It is the same construction as described for line 43 of Fig. l. In this case it is necessary to relieve the worm thread, starting at the described interference line.

Diagram Fig. 12 similarly characterizes an embodiment that approximates a worm drive where. a definite interference line is assumed on the wormgear tooth. Point 40 of this interference line moves about the wormgear axis, in the direction of the projected worm axis 25. Here a path of contact 75 is required in the pitch plane 37'. Its inclination i is larger than the helix angle h of the wormgear teeth, and may be assumed approximately according tothe formula rant- 2 tan h 9. given in application Serial No. 682,804. This requires a basic member whose axis 76 is inclined to the projected worm axis 25 at an angle 7 smaller than inclination 1'.

Here the wormgear teeth should be relieved, starting at the interference line that passes through point 40.

In the instance illustrated in Fig. 12 the basic member is a circular rack 77 having conical tooth surfaces 77. Its axis 76 lies in the plane of projection of toothnormal 50 at point 40. The drawing plane coincides with the pitch plane 37 that is tangent to the contacting pitch surfaces at point .0. To achieve a path of contact 75 in this plane, a line 43" may be drawn at right angles to axis 76 and at such a distance from pitch point 40 that the distance 44"-45" is equal to the center distance of the worm gearing. Points 44-" and 45" are the intersection points of line 43" with the projected axes 25, 26 of the worm and wormgear. Line 43" intersects the path of contact 75 at a point 78. The distance 78-80 of point 78 from point 89 represents the pitch radius of the circular rack'77, here assumed at the root of the circular teeth. Distance 44"78 represents the pitch radius of the worm. To end up with a given tooth ratio n/N the helix angle it may be selected according to the formula tan 3 h= /2 n/N when the axes 25, 26 are at right angles and when the above equation for tan i is to be exactly fulfilled. In general it may also be determined by trial. a

The useful part of the path of contact 75 and of path 35 are'shown in full lines, the remainder in dotted lines.

Fig. 13 is generally similar to Fig. ll, but shows a path of contact 35 less inclined to the direction of the worm axis 25 than path 35. It can be demonstrated mathematically that this produces an interference line 81 inclined from the projected wormgear axis 26 to the side shown. In this case both the worm and the wormgear should be relieved. Exact adherence to the first described embodiment is then not compulsory. Similarly the path of contact 75 of Fig. 12 may be materially departed from when relief is applied to both the worm and wormgear. Relief should start at the lines that correspond to the tooth-surface normal 58 at pitch point 40.

The embodiment of Figures 14 to 18 is similar to the one described with Fig. 12, but uses a basic member 83 having an involute helical thread 84 instead of the circular tooth surfaces 77. Preferably the position of its axis 85 and the pitch are so determined that member 83 contains a single thread. 7

To achieve a path of contact 75in pitch plane 37 the following construction may be used: Let r and R denote the pitch radii of the worm 93 and wormgear 94, that is the distances of pitch point 40 from the worm axis 25 and from the wormgear axis 26 respectively. Point 86 (Fig; 14) is then plotted on line 25 at a distance (r+R) from point 40, and point 87 at a distance R from point 46. The intersection point 89 of vertical 88 through 87 with path 75 is connected with point 86; and a perpendicular -90 is drawn to the connecting line 86-39. It intersects it at point 90, and represents the direction of the axis 85 of the basic helicoid. The offset 86-92 of axis 85 from the worm axis 25 is determined by projecting point 90 to line 25. Axis 85 intersects the center line 36 at 92. The tooth number of the helical member 83 can then be determined from the position of its axis and the direction of the tooth normal. atpitch point 40.

Ordinarily the tooth number so determined is not an integral number. A different pitch radius r is then assumed. R is the given center distance minus r, and the determination is repeated until the member contains a single thread, using a known method of interpolation.

. i0 Path of contact 75 is inclined at an angle i which approximately corresponds to the formula tan i= 2 tan h Normals 50, 50c, 562 are lines of the surface of action. They pass through points 40, 400, we of path 75, and are tilted with respect to each other about axis of the basic helical member 83, see Fig. 17. They include a constant angle with axis 85.

Here the pitch point 40 is placed adjacent the root surface of the worm. The extended surface of action intersects center line 36 at pitch point 40, preferably at a distance from the root surface of the wormgear larger than the working depth (95, Fig. 14) of the teeth. In this way the region of mesh is increased. The relieved portion 96 of a wormgear tooth is shown covered with dots in Fig. 16. It is smaller than the working portion. The working portion and relieved portion meet in a line which in Fig. 16 nearly coincides with the projection of normal 56, and which extends obliquely from the outside surface of the wormgear to its root surface. The end of said line adjacent said root surface has a larger distance from the central plane of rotation of the wormgear than the end at said outside surface.- The said plane contains center line 36 and worm axis 25.

Wormgear 94 may be produced with a helical hob that represents member 83. The relieved part of the wormgear teeth may be produced either in a separate operation, as a roughing cut, or by portions built into the helical hob. r

The worm 93 may be cut for instance with a gearshaped cutter (Figs. 10 and 18) which, while the worm rotates, turns on its axis and is fed to follow the surface of action. The latter extends about axis 85 at a substantially constant distance therefrom. In the middle position, shown in full lines, the cutter 186 acts along a line of action 50 that coincides with the surface normal at pitch point 40. To act along a normal such as 50a the cutter is fed about axis 85 and along axis 85 so that its pitch point coincides with point 98 (Fig. 17). This is the point at which normal 50:: intersects the cylindrical pitch surface 99 of member 83. In other words, cutter 106 is fed through an angle 4ii-85-98 about axis 85 and fed along said axis. The cutter is then in the position shown in dotted lines 199.

The two sides of the threads are alike. The work ing portions of both sides may be produced during feed in one direction about and along axis 85. For further details of production reference is made to my application Method and Machine for Producing Teeth and Threads filed February 24, 1958, Serial No. 716,957.

Shaft angles differing from a right angle may also be used. Such shaft angles generally cause less tooth interference than right shaft angles, so that less or no tooth relief is required to prevent interference. The geometric determination of the basic member from a given path of. contact remains as described.

While the invention has been described in connection with several different embodiments thereof, it will be understood that it is capable of further modification, and this application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice in the art to which the invention pertains, and as fall within the scope of the invention or the limits of the appended claims.

I claim:

1. Worm gearing comprising a throated worm and a wormgear having a root surface of concave axial profile, said worm and wormgear being at least approximately conjugate to the tooth surfaces of a basic member adapted to contact the worm and wormgear along lines of varying shape, which are the same lines along which the worm and wormgear contact each other, said basic member having all along its contacting tooth surfaces a profile of constant shape and constant radial position with respect to the axis of said member.

2. Worm gearing according to claim 1, wherein said tooth surfaces have a constant normal base pitch.

3. Worm gearing according to claim 2, wherein said tooth surfaces of the basic member are involute helicoids.

4. Worm gearing whose two rotating elements are a throated worm and a wormgear meshing therewith, said two elements being formed conjugate to the tooth surfaces of a cylindrical member, one of said elements being conjugate to said member embodied as an external member, the other element being conjugate to an imaginary internal member which is approximately the counterpart of said external member, the inside diameter of said internal member being smaller than the mean root diameter of said other element.

5. Worm gearing whose two rotating elements are a throated worm and a wormgear meshing therewith, one of said elements being fully conjugate to the tooth surfaces of an imaginary internal cylindrical member of smaller inside diameter than the mean root diameter of said one element, said tooth surfaces having a constant profile along their length, and the axis of said member being angularly disposed to and offset from each of the axes of said elements.

6. Worm gearing according to claim 4, wherein the worm is fully conjugate to a. helical member whose axis is angularly disposed to the axes of the worm and wormgear and intersects the center line of the wormgear pair at a point between the intermeshing teeth and the axis of the wormgear, said member having helical teeth with involute tooth sides.

7. Worm gearing according to claim 6 wherein said member has a fractional number of teeth, so that the circumference of said member is not an integral multiple of its circular pitch.

8. Worm gearing comprising a throated worm and a wormgear having a root surface of concave axial profile, said wormgear being formed fully conjugate to and adapted to mesh with line contact with an imaginary internal cylindrical member having involute teeth and having a smaller inside diameter than the mean root diameter of said wormgear, the axis of said member being angularly disposed to and offset from the axis of said wormgear, and said worm being formed conjugate to said wormgear to transmit uniform motion between them.

9. Worm gearing comprising a throated worm and a wormgear having a root surface of concave axial profile, said worm being formed fully conjugate to a rotary member containing helical teeth, the axis of said member being offset from the axis of said worm and including an angle with the direction of the worm axis differing from the shaft angle of the worm gearing, the thread sides of said worm having a changing inclination to planes perpendicular to the worm axis, each of said thread sides being composed of a working portion and of a relieved portion disposed adjacent the thread-side end of least inclination.

10. Worm gearing according to claim 9, wherein the working portion and the relieved portion of a thread side meet in a spiral line whose inner end, adjacent the thread.

bottom, has a larger distance from the central plane of rotation of the worm than the outer end of said spiral line.

ll. Worm gearing according to claim 9, wherein said relieved portion of a thread side is longer at the outside surface of the worm than adjacent the root surface of the Worm.

12. Worm gearing comprising a throated worm and a wormgear having a root surface of concave axial profile, said worm and wormgear being conjugate to each otherand suited to transmit uniform motion between them, their tooth shape'corresponding to a surface of action that comes closer to the center line of the worm gearing at the outside surface of the worm thread than at the portions adjacent the root surface of the worm.

13. Worm gearing comprising a throated worm and a wormgear having a root surface of concave axial profile, said worm wormgear meshing along a surface of action which, at least when extended, intersects the center line of the worm gearing at the pitch point, said pitch point being disposed adjacent the outside surface of the worm at a larger distance from the root surface of the worm than the working depth of the thread.

14. Worm gearing according to claim 4, wherein the wormgear is fully conjugate to and adapted to mesh with line contact with an external cylindrical member, the axis of said member being angularly disposed to and offset from the axes of said worm and wormgear and intersecting the center line of the worm gearing at a point between the intermeshing teeth and the axis of the worm, the position of said axis being selected to effect a surface of action of the worm and wormgear extending diagonally across the zone of intermeshing teeth, at an average angle to the direction of the worm axis larger than the mear inclination of the wormgear teeth to the direction of the wormgear axis.

15. Worm gearing according to claim 4, wherein the worm is fully conjugate to and adapted to mesh with line contact with an imaginary internal cylindrical member whose axis intersects said worm, said member having a smaller insidediameter than the root diameter of said worm at its throat.

l6. Worm gearing according to claim 14, wherein said cylindrical member is a circular rack having conical tooth sides.

17. Worm gearing according to claim 14, wherein said cylindrical member is a worm containing a single helical thread.

18. Worm gearing according to claim 14, wherein the surface of action of the wormgear pair, at least when extended, intersects the center line of said pair at a point adjacent the root surface of the worm, at a distance larger than the working depth of the teeth from the root surface of the wormgear.

19. Worm gearing according to claim 18, wherein each tooth side of the worm gear contains a working portion and a relieved portion, said portions meeting in a line extending obliquely from the outside surface of the wormgear towards its root surface, the end of said line adjacent said root surface having a larger distance from the central plane of rotation of the wormgear than the end at said outside surface.

References Cited in the file of this patent UNITED STATES PATENTS 1,683,163 Cone Sept. 4, 1928 1,694,028 Sildhaber Dec. 4, 1928 1,746,722 Trbojevich Feb. 11, 1930 1,792,782 Trbojevich Feb. 17, 1931 1,815,685 Trbojevich July 21, 1931 1,902,683 Wildhaber Mar. 21, 1933 1,903,318 Wildhaber Apr. 4, 1933 2,069,433 Wildhaber Feb. 2, 1937 2,279,414 Scott Apr. 14, 1942 2,432,246 Mackmann et a1. Dec. 9, 1947 2,619,845 Mackmann et a1. Dec. 2, 1952 

